Coupling chemical diffusion and mechanical deformation with application to plagioclase
Seminar by post-doc Xin Zhong
Plagioclase rim (left) and grain (right) showing CaO concentration variation. In the plagioclase rim, the pressure gradient from high (HP) to low (LP) maintains the concentration variation even at temperature >800 degree C over geological time.
Chemical diffusion is a critical process happening in metamorphic rocks and has profound significance in deciphering metamorphic history recorded by minerals showing concentration zoning patterns. However, in widely-used Fick’s diffusion model, the coupling effect of mechanical deformation on chemical diffusion is not considered. In this talk, I will show a coupled model for chemical diffusion and mechanical deformation developed in analogy to the studies of poroelasticity and thermoelasticity. Nondimensionalization of the governing equations yields a controlling dimensionless parameter, the Deborah number, given by the ratio of the characteristic time for pressure relaxation and concentration homogenization. Using the Deborah number two types of plausible chemical zonation are distinguished, i.e. diffusion controlled, and mechanically controlled. The transition between these two types of chemical zonation is determined at the conditions where the Deborah number equals one.
This model is applied to chemically zoned plagioclase assuming homogeneous initial pressure. Using thermodynamic data, an experimentally derived diffusion coefficient and viscous flow law for plagioclase, the numerical simulations show that up to ∼0.6 GPa grain-scale pressure variation is generated during the diffusion–deformation process. Due to the mechanical–chemical coupling, the pressure variations maintain the chemical zonation longer than predicted by the classical diffusion model. The fully coupled mechanical–chemical model provides an alternative explanation for the preservation of chemically zoned minerals.